There are 1bd condos available which fall in the district, if you would consider those. Also, if you do decide to go with renting as an alternative, as suggested, you check to see which properties fall into the 3rd st school district here: http://search.lausd.k12.ca.us/cgi-bin/fccgi.exe?w3exec=schfinder0
Another suggestion is to work with a Realtor who can help you find pocket listings in the area which may not be listed on the mls. I do this for my clients all the time. Please call if you need help. Thanks.
Prudential California Realty
The best option is going to be a house (fixer) or a condo. Please send me your email and I'll forward you some options.
The Carrabba Group
Keller Williams Hollywood Hills